pw_root {VirtualPop}

The Function for which the Root is Sought.

Description

The function pw_root() specifies the mathematical function g(t). The equation to be solved is g(t)=0, with g(t) the cumulative hazard function of the piecewise exponential distribution + log(u) with u a random draw from standard uniform distribution (see vignette "Piecewise_exponential", Section 2.2.4).

Usage

pw_root(t, breakpoints, rates, uu)

Arguments

t

Vector of durations for which the equation g(t)=0 should be solved.

breakpoints

Breakpoints

rates

Piecewise-constant rates

uu

Random draw from standard uniform distribution.

Details

pw_root is an argument of the function uniroot() of base R (argument "f"). It is required by uniroot(). The function uniroot() is called by r.pw_exp(). See also Functions H_pw() and r.pw_exp().

Value

Vector of differences between cumulative hazard and -log(uu) for different values of t.

Examples

breakpoints <- c(0, 10, 20, 30, 60)
rates <- c(0.01,0.02,0.04,0.15)
z <- VirtualPop::pw_root (t= c(10,18.3,23.6,54.7),breakpoints,rates,uu=0.43)